April 13 - 24 Instructor : Brian Powers 19 . 1 Statistical Hypotheses

We never know with certainty the validity of a hypothesis unless we examine the entire population. What we can say is the probability of observing our sample data if the hypothesis was correct. If this probability is extremely small we would argue that it is unlikely that the hypothesis is valid. We then “reject the hypothesis.” The null hypothesis (denoted H0) is the hypothesis we test, the rejecion of which leads us to acceptance of the alternative hypothesis (Denoted H1 or HA or Ha depending on the book). If there is sufficient evidence in the data in favor of the alternative hypothesis, we reject H0, otherwise we say that we fail to reject H0. We do not say that we “accept H0”. The null hypothesis is the “status quo”, it is what we assume to be true unless we can prove otherwise.